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Department of Manufacturing and Mechanical Engineering Technology


This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation.

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c 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ( Publisher’s version of record:

Publication Title

Journal of Marine Science and Engineering

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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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